1. **State the problem:** Simplify the expression $$\left(\frac{5}{9}x + \frac{1}{8}\right) + \left(\frac{7}{12}x - \frac{1}{8}\right)$$. 2. **Write the expression without parentheses:** $$\frac{5}{9}x + \frac{1}{8} + \frac{7}{12}x - \frac{1}{8}$$ 3. **Combine like terms:** - Combine the $x$ terms: $$\frac{5}{9}x + \frac{7}{12}x$$ - Combine the constants: $$\frac{1}{8} - \frac{1}{8}$$ 4. **Find common denominators to add the $x$ terms:** - The denominators are 9 and 12. - The least common denominator (LCD) is 36. 5. **Convert each fraction to have denominator 36:** $$\frac{5}{9}x = \frac{5 \times 4}{9 \times 4}x = \frac{20}{36}x$$ $$\frac{7}{12}x = \frac{7 \times 3}{12 \times 3}x = \frac{21}{36}x$$ 6. **Add the $x$ terms:** $$\frac{20}{36}x + \frac{21}{36}x = \frac{20 + 21}{36}x = \frac{41}{36}x$$ 7. **Simplify the constants:** $$\frac{1}{8} - \frac{1}{8} = 0$$ 8. **Final simplified expression:** $$\frac{41}{36}x + 0 = \frac{41}{36}x$$ 9. **Check the options:** None of the options exactly match $$\frac{41}{36}x$$, so let's verify the original problem carefully. **Re-examining the problem:** The user wrote the expression as: $$(\frac{5}{9}x + \frac{1}{8}) + (\frac{7}{12}x - \frac{1}{8})$$ Adding the constants cancels out to zero. **Therefore, the simplified expression is:** $$\frac{41}{36}x$$ Since none of the options match $$\frac{41}{36}x$$, let's check if the user made a typo or if the options are approximate. **Note:** Option C is $$\frac{71}{63}x$$. Simplify $$\frac{71}{63}$$: $$\frac{71}{63} = \frac{71}{63}$$ (cannot simplify further). Convert $$\frac{41}{36}$$ to decimal: approximately 1.1389. Convert $$\frac{71}{63}$$ to decimal: approximately 1.1269. They are close but not equal. **Conclusion:** The simplified expression is $$\frac{41}{36}x$$. **Answer:** $$\boxed{\frac{41}{36}x}$$